Hi,
I can confirm there's no build-in feature to realize your request, we can't specify on which day of a week Out of Office is turned on, it is a product limitation so far.
As far as I can tell, we can use a rule with some script as a workaround. The condition can be something like "any messages received on a certain day", then the action is sending an automatic reply to the sender.
Anyway, the rule may need some help about the script, as we don't provide suggestions about script in this forum, if you'd like to use this method, you can ask the question in Outlook for Developers forum:
https://social.msdn.microsoft.com/Forums/office/en-US/home?forum=outlookdev
Regards,
Melon Chen
TechNet Community Su